Question

因式分解，要过程！

^是几次方的意思
1. （6x^3y^4z-4^2y^3z+2xy^3)÷2xy^3
2. (-a^2b-ab^2)÷(-ab)
3. [(x+y)^2-(x-y)^2]÷xy
4. [6(a-2)^5-15(a-2)^4]÷3(a-2)
5. [(x+3)^2+(x+3)(x-3)]÷2x
6. (16a^4 b^5 c^3-12a^3 b^2 c^2+8a^2 b^3)÷(-2ab)^2

拜托了 ，一定要有过程啊！最好快一些，好的加分，虽然不多...

Answer 1

1. （6x^3y^4z-4x^2y^3z+2xy^3)÷2xy^3
=2xy^3（6x^2yz-4xz+1)÷2xy^3
=6x^2yz-4xz+1

2. (-a^2b-ab^2)÷(-ab)
=(-ab)(a+b)÷(-ab)
=a+b

3. [(x+y)^2-(x-y)^2]÷xy
={ [(x+y)-(x-y)][(x+y)+(x-y)]}÷xy

=[(x+y-x+y)(x+y+x-y)]÷xy

=4xy÷xy
=4

4. [6(a-2)^5-15(a-2)^4]÷3(a-2)
=3(a-2)[2(a-2)^4-5(a-2)^3]÷3(a-2)
=2(a-2)^4-5(a-2)^3

5. [(x+3)^2+(x+3)(x-3)]÷2x
= [(x+3)(x+3+x-3)]÷2x
= 2x(x+3)÷2x

=x+3

6. (16a^4 b^5 c^3-12a^3 b^2 c^2+8a^2 b^3)÷(-2ab)^2
=(16a^4 b^5 c^3-12a^3 b^2 c^2+8a^2 b^3)÷(4a^2b^2)
=4a^2b^2(4a^2 b^3 c^3-3a c^2+2b)÷(4a^2b^2)

=4a^2 b^3 c^3-3a c^2+2b